The Permanent Strain in a Uniform Bar Due to Longitudinal Impact

Abstract

Abstract A method is presented for predicting the final strained state of a long uniform bar or wire of ductile material that is subjected to a longitudinal impact of finite duration during which the impact stress is constant and exceeds the yield strength. It is shown that for a long specimen this corresponds to giving the point of impact a constant velocity during the impact interval. (After this interval the stress at the end of the member is zero, but not its particle velocity.) It is also shown that the final unit strains are greatest immediately adjacent to the impact point and are constant over a finite length of specimen. Following this region of constant residual strain is a region, also of finite length, in which the permanent strain decreases steadily with distance from the end of the specimen. At the end of this there is another zone of constant permanent strain, which is followed by one of decreasing permanent strain, and so on. It is shown that there is a definite relation between the stress history at a point of a specimen and the velocity of that point—this relation is given. It is demonstrated that in tensile impact a critical velocity of impact can be defined, corresponding to the ultimate strength of the material. At impact velocities greater than this critical velocity, rupture occurs quickly and close to the point of impact so that the remainder of the specimen does not receive large deformations. Thus the energy required to break a specimen in tension is less at supercritical than at subcritical impact velocities.